7. Solve |3x – 2| = |x + 1|

6. A prism has bases that are equilateral triangles with sides lengths of 10 inches and a length of 30 inches.

eimsori [14]

Answer:

The volume of the prism is $1,299\ in^{3}$

Step-by-step explanation:

we know that

The volume of the prism is equal to

$V=BL$

where

B is the area of the triangular base

L is the length of the prism

we have

$L=30\ in$

The area of a equilateral triangle is equal to

$B=\frac{1}{2}(10)^{2} sin(60\°)$

$B=25\sqrt{3}\ in^{2}$

substitute

$V=(25\sqrt{3})(30)=1,299\ in^{3}$

8 0

3 years ago

Max's car holds 18 gallons of gasoline.Driving on the highway, the car uses approximately 2 gallons per hour. Let h represent th

balandron [24]

So amount minused=hours driven times gallons per mile=h times 2 or 2h

so we minus 2h

18-2h is the expression

8 0

3 years ago

a snowball is rolled down a giant hill. the radius of the snowball grows. every second the radius increases by 0.36 inches. four

Bad White [126]

Based on the fact that the radius of the snowball increases by 0.36 inches every second, the linear function can be found to be y = 0.36x + 1.66

<h3>How to find the linear function?</h3>

The linear function is the function that shows how to change in the rate of the independent variable would affect the rate of change in the dependent variable.

The linear function takes the form:

y = mx + b

y = dependent variable

m = slope or change in radius of snowball

x = seconds

b = y-intercept

Solving for the y-intercept gives:

3.1 = 0.36(4) + b

b = 3.1 - 1.44

= 1.66

The linear function is therefore:

y = 0.36x + 1.66

Find out more on linear functions at brainly.com/question/28029655

#SPJ1

3 0

1 year ago

When the function f(x) = 6(9)x is changed to f(x) = 6(9)x + 1, what is the effect? (5 points) There is no change to the graph be

amm1812

Answer:

The y-intercept is 1 space higher.

Step-by-step explanation:

y goes up by 1.

4 0

3 years ago

Read 2 more answers

The random variable x has the following probability distribution: x f(x) 0 .25 1 .20 2 .15 3 .30 4 .10 a. Is this probability di

Reptile [31]

Answer and Explanation:

Given : The random variable x has the following probability distribution.

To find :

a. Is this probability distribution valid? Explain and list the requirements for a valid probability distribution.

b. Calculate the expected value of x.

c. Calculate the variance of x.

d. Calculate the standard deviation of x.

Solution :

First we create the table as per requirements,

x P(x) xP(x) x² x²P(x)

0 0.25 0 0 0

1 0.20 0.20 1 0.20

2 0.15 0.3 4 0.6

3 0.30 0.9 9 2.7

4 0.10 0.4 16 1.6

∑P(x)=1 ∑xP(x)=1.8 ∑x²P(x)=5.1

a) To determine that table shows a probability distribution we add up all five probabilities if the sum is 1 then it is a valid distribution.

$\sum P(X)=0.25+0.20+0.15+0.30+0.10$

$\sum P(X)=1$

Yes it is a probability distribution.

b) The expected value of x is defined as

$E(x)=\sum xP(x)=1.8$

c) The variance of x is defined as

$V=\sum x^2P(x)-(\sum xP(x))^2\\V=5.1-(1.8)^2\\V=5.1-3.24\\V=1.86$

d) The standard deviation of x is defined as

$\sigma=\sqrt{V}$

$\sigma=\sqrt{1.86}$

$\sigma=1.136$

5 0

3 years ago